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|Symmetry group||D3d, [2+,6], (2*3), order 12|
|Rotation group||D3, [2,3]+, (223), order 6|
|Dual polyhedron||trigonal antiprism|
Six identical rhombic faces can construct two configurations of trigonal trapezohedra. The acute or prolate form has three acute angles corners of the rhombic faces meeting at two polar axis vertices. The obtuse or oblate or flat form has three obtuse angle corners of the rhombic faces meeting at the two polar axis vertices.
The trigonal trapezohedra is a special case of a rhombohedron. A general rhombohedron allows up to three types of rhombic faces.
A trigonal trapezohedron is a special kind of parallelepiped, and are the only parallelepipeds with six congruent faces. Since all of the edges must have the same length, every trigonal trapezohedron is also a rhombohedron.
A golden rhombohedron is one of two special case of the trigonal trapezohedron with golden rhombus faces. The acute or prolate form has three acute angles corners of the rhombic faces meeting at two polar axis vertices. The obtuse or oblate or flat form has three obtuse angle corners of the rhombic faces meeting at the two polar axis vertices. Cartesian coordinates for a golden rhombohedron with one pole at the origin are:
- (1/, 2/, 0)
- (1/, φ − 1/, φ/)
The rhombic hexecontahedron can be constructed by 20 acute golden rhombohedra meeting at a point.
|Family of trapezohedra V.n.3.3.3|
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